Scanning optical apparatus

ABSTRACT

A scanning optical apparatus includes a light source, a deflecting element for deflecting a beam of light emitted from the light source, an optical device for causing the beam of light emitted from the light source to be imaged into a linear shape long in the main scanning direction on the deflecting surface of the deflecting element. The optical device is comprised of a first optical element and a second optical element, and a third optical element for causing the beam of light deflected by the deflecting element to be imaged into a spot-like shape on a surface to be scanned. The third optical element includes a single lens, the opposite lens surfaces of which both include a toric surface of an aspherical surface shape in the main scanning plane, the curvatures of the opposite lens surfaces in the sub scanning plane being continuously varied from the on-axis toward the off-axis in the effective portion of the lens.

This application is a division of application Ser. No. 08/951,635 filedOct. 17, 1997, now U.S. Pat. No. 8,213,068, which is a continuation ofapplication Ser. No. 08/607,169 filed Feb. 26, 1996, now abandoned,which is a continuation-in-part of application Ser. No. 08/522,118 filedAug. 31, 1995, U.S. Pat. No. 5,818,505.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a scanning optical apparatus and a multibeamscanning optical apparatus, and particularly to a scanning opticalapparatus and a multibeam scanning optical apparatus suitable for use,for example, in an apparatus such as a laser beam printer (LBP) or adigital copying apparatus having the electrophotographic process adaptedto deflect and reflect a beam of light optically modulated and emittedfrom light source means by a light deflector (deflecting element)comprising a rotatable polygon mirror or the like, thereafter opticallyscan a surface to be scanned through an imaging optical system havingthe fθ characteristic (fθ lens) and record image information.

2. Related Background Art

Heretofore, in the scanning optically apparatus of a laser beam printeror the like, a beam of light optically modulated and emerging from lightsource means in conformity with an image signal has been periodicallydeflected by a light deflector comprising, for example, a rotatablepolygon mirror and has been converged into a spot-like shape on thesurface of a photosensitive recording medium (photosensitive drum)having the fθ characteristic, and that surface has been opticallyscanned to thereby effect image recording.

FIG. 1 of the accompanying drawings is a schematic view of the essentialportions of a scanning optical apparatus according to the prior art.

In FIG. 1, a divergent beam of light emitted from light source means 61is made into a substantially parallel beam of light by a collimator lens62, and the beam of light (the quantity of light) is limited by a stop63 and enters a cylindrical lens 64 having predetermined refractivepower only in a sub scanning direction. Of the parallel beam of lighthaving entered the cylindrical lens 64, that part in a main scanningsection intactly emerges in the state of a parallel beam of light. Also,that part in a sub scanning section converges and is imaged as asubstantially linear image on the deflecting surface (reflectingsurface) 65 a of a light deflector 65 comprising a rotatable polygonmirror. Here, the main scanning section refers to a beam section thebeam of light deflected and reflected by the deflecting surface of thelight deflector forms with time. Also, the sub scanning section refersto a section containing the optical axis of an fθ lens and orthogonal tothe main scanning section. The beam of light deflected and reflected bythe deflecting surface 65 a of the light deflector 65 is directed ontothe surface of a photosensitive drum 68 as a surface to be scannedthrough an imaging optical system (fθ lens) 66 having the fθcharacteristic, and the light deflector 65 is rotated in the directionof arrow A to thereby optically scan the surface of the photosensitivedrum 68 and effect the recording of image information.

To effect the highly accurate recording of image information in ascanning optical apparatus of this kind, it is necessary that curvatureof image field be well corrected over the entire area of a surface to bescanned and a spot diameter be uniform and that the angle and imageheight of the incident light have distortion (fθ characteristic) inwhich they are in a proportional relation. A scanning optical apparatussatisfying such optical characteristics or the correcting optical system(fθ lens) thereof has heretofore been variously proposed.

On the other hand, with the tendency of laser beam printers, digitalcopying apparatuses, etc. toward compactness and lower cost, similarthings are required of the scanning optical apparatus.

As an apparatus which makes these requirements compatible, a scanningoptical apparatus in which the fθ lens is comprised of a single lens isvariously proposed, for example, in Japanese Patent Publication No.61-48684, Japanese Laid-Open Patent Application No. 63-157122, JapaneseLaid-Open Patent Application No. 4-104213, Japanese Laid-Open PatentApplication No. 4-50908, etc.

Of these publications, in Japanese Patent Publication No. 61-48684 andJapanese Laid-Open Patent Application No. 63-157122, a concave singlelens as on fθ lens is used on the light deflector side to converge aparallel beam of light from a collimator lens on the surface of arecording medium. Also, in Japanese Laid-Open Patent Application No.4-104213, as fθ lenses, a concave single lens and a toroidal-surfacedsingle lens are used on the light deflector side and the image planeside, respectively, to make a beam of light converted into convergentlight by a collimator lens enter the fθ lenses. Also, in JapaneseLaid-Open Patent Application No. 4-50908, a single lens introducing ahigh-order aspherical surface into a lens surface is used as an fθ lensto make a beam of light converted into convergent light by a collimatorlens enter the fθ lens.

However, in the scanning optical apparatuses according to the prior artdescribed above, according to Japanese Patent Publication No. 61-48684,curvature of image field in the sub scanning direction remains and aparallel beam of light is imaged on the surface to be scanned, and thishas led to the problem that the distance from the fθ lens to the surfaceto the scanned becomes a focal length f and is long and it is difficultto construct a compact scanning optical apparatus. In Japanese Laid-OpenPatent Application No. 63-157122, the thickness of the fθ lens is great,and this has led to the problem that manufacture by molding is difficultand this makes a factor of increased cost. Japanese Laid-Open PatentApplication No. 4-104213 has suffered from the problem that distortionremains. In Japanese Laid-Open Patent Application No. 4-50908, an fθlens having a high-order aspherical surface is used and aberrations arecorrected well, but there has been the problem that jitter of a periodcorresponding to the number of polygon surfaces occurs due to themounting error of a polygon mirror which is a light deflector.

Further, problems common to these fθ lenses each comprised of a singlelens has included the problem that due to the non-uniformity of thelateral magnification in the sub scanning direction between the lightdeflector and the surface to be scanned, the spot diameter in the subscanning direction changes depending on image height.

FIGS. 2A and 2B of the accompanying drawings are cross-sectional viewsof the essential portions of a single beam scanning optical apparatus inthe main scanning direction and the sub scanning direction,respectively, and show changes in the spot diameter (F number) in thesub scanning direction due to image height. In these figures, the sameelements as the elements shown in FIG. 1 are given the same referencenumerals.

Usually, in a plane inclination correcting optical system, it isnecessary to bring the deflecting surface of a light deflector and asurface to be scanned into an optically conjugate relation (imagingrelation) in order to optically correct the plane inclination of thedeflecting surface. Accordingly, in an fθ lens having a predeterminedlens shape in the main scanning section as in the aforedescribedexamples of the prior art, lateral magnification is high on the axis(on-axis beam 21) as indicated at (1) in FIG. 28, and lateralmagnification becomes low off the axis (most off-axis beam 22) asindicated at (2) in FIG. 2B (there is also a case where this becomesconverse depending on the lens shape in the main scanning section).

Thus, irregularity occurs to the lateral magnification in the subscanning direction depending on the lens shape of the fθ lens in themain scanning plane thereof and a change in the spot diameter in the subscanning direction due to image height occurs.

On the other hand, the ability of higher speed scanning is required of ascanning optical apparatus for use in an LBP because of the tendency ofthe LBP toward higher speed and higher accuracy, and from limitationssuch as the number of revolutions of a motor which is scanning means andthe number of surfaces of a polygon mirror which is deflecting means,particularly the demand for a multibeam scanning optical apparatuscapable of scanning a plurality of beams of light at a time is growing.

The above-described non-uniformity of the lateral magnification in thesub scanning direction makes the curve of the scanning line when theposition of a light source (light source unit) is off the optical axisin Z direction indicated in FIGS. 2A and 2B and therefore, an opticalsystem such as a multibeam scanning optical system (multibeam scanningoptical apparatus) which scans a surface to be scanned at a time by theuse of a plurality of beams of light off the optical axis has sufferedfrom the problem that the scanning line bends on the surface to bescanned and as a result, the deterioration of image quality due to pitchirregularity occurs.

SUMMARY OF THE INVENTION

It is a first object of the present invention to provide a compactscanning optical apparatus suitable for highly accurate printing inwhich when a beam of light from a light source converted by a collimatorlens or the like is to be imaged on a surface to be scanned by an fθlens through a light deflector, the lens shape (the main scanning planeshape) of the fθ lens in the main scanning plane thereof is optimized tothereby correct curvature of image field, distortion, etc. and thenon-uniformity of lateral magnification in the sub scanning directionbetween the light deflector and the surface to be scanned is eliminatedby only the lens shape (the sub scanning plane shape) in the subscanning plane, independently of the lens shape in the main scanningplane, whereby any change in F number (F No.) in the sub scanningdirection due to image height, i.e., any change in spot diameter, can besuppressed.

It is a second object of the present invention to provide a compactmultibeam scanning optical apparatus suitable for highly accurateprinting in which a plurality of beams of light from a light sourceconverted by a collimator lens or the like is to be imaged on a surfaceto be scanned by an fθ lens through a light deflector, the lens shape(the main scanning plane shape) of the fθ lens in the main scanningplane thereof is optimized to thereby correct curvature of image field,distortion, etc. and the non-uniformity of lateral magnification in thesub scanning direction between the light deflection and the surface tobe scanned is eliminated by only the lens shape (the sub scanning planeshape) in the sub scanning plane, independently of the lens shape in themain scanning plane, whereby any change F number (F No.) in the subscanning direction in spot diameter, can be suppressed and a beam oflight from the light source which is off the optical axis in the subscanning direction can also be scanned highly accurately without thecurve of the scanning line occurring.

The scanning optical apparatus of the present invention is

(1-1) a scanning optical apparatus in which a beam of light emitted fromlight source means is imaged into a linear shape long in the mainscanning direction on the deflecting surface of a deflecting elementthrough a first optical element and a second optical element and thebeam of light deflected by the deflecting element is imaged into aspot-like shape on a surface to be scanned through a third opticalelement to thereby scan the surface to be scanned, characterized in thatthe third optical element comprise a single lens, the opposite lenssurfaces of the single lens both comprise a tori surface of anaspherical shape in the main scanning plane, and the curvature thereofin the sub scanning section is continuously varied from the on-axistoward the off-axis in the effective portion of the lens to therebysuppress any change of F number in the sub scanning direction due to theimage height of the beam of light incident on the surface to be scanned.

Particularly, it is characterized in

(1-1-1) that the light source means has a plurality of light sourcemeans has a plurality of light source units capable of beingindependently modulated,

(1-1-2) that when the curve amounts of the loci, in the main scanningplane, of the front side principal plane and the rear side principalplane of the third optical element in the sub scanning direction (thedifference in the direction of the optical axis between the mostoff-axis principal plane position and the on-axis principal planeposition) are xm and xu, respectively, the following condition xm≦dx≦xu,is satisfied:

where

${dx} = \frac{{Ipri} \cdot {{Epri}\left( {{\cos\;\theta\;{img}} - {\cos\;\theta\;{por}}} \right)}}{{{{Ipri} \cdot \cos}\;\theta\;{por}} + {{{Epri} \cdot \cos}\;\theta\;{img}}}$

-   -   Ipri: the distance from the deflecting surface of the deflecting        element in the on-axis beam to the front side principal plane in        the sub scanning direction;    -   Epri: the distance from the rear side principal plane in the sub        scanning direction in the on-axis beam to the surface to be        scanned;    -   θpor: the angle formed in the main scanning plane by the most        off-axis beam deflected by the deflecting element with respect        to the optical axis;    -   θimg: the angle formed in the main scanning plane by the most        off-axis beam incident on the surface to be scanned with respect        to the optical axis;

(1-1-3) that the sign of the curvature of at least one of the oppositelens surfaces of the single lens constituting the third optical elementin the subscanning plane is reversed from the on-axis toward theoff-axis; and

(1-1-4) that the third optical element is made by plastic molding; or

(1-1-5) that the third optical element is made by glass molding.

The multibeam scanning optical apparatus of the present invention is

(2-1) a multibeam scanning optical apparatus in which a plurality ofindependently modulated beams of light emitted from light source meansare imaged into linear shapes long in the main scanning direction on thedeflecting surface of a deflecting element through a first opticalelement and a second element and the plurality of beams of lightdeflected by the deflecting element are imaged into a spot-like shape ona surface to be scanned through a third optical element to thereby scanthe surface to be scanned,

characterized in that the third optical element comprises a single lens,and the curvatures of the opposite lens surfaces of the single lens inthe sub scanning direction are continuously varied from the on-axistoward the off-axis to thereby suppress any change of F number in thesub scanning direction due to the image height of the beam lightincident on the surface to be scanned.

Particularly, it is characterized in

(2-1-1) that when the maximum value and minimum value of the F number ofthe beam of light incident on the surface to be scanned in the subscanning direction are Fmax and Fmin, respectively, the curvatures ofthe opposite lens surfaces of the single lens constituting the thirdoptical element in the sub scanning direction are continuously variedfrom the on-axis toward the off-axis so as to satisfy the condition thatFmin/Fmax≧0.9,

(2-1-2) that the sign of the curvature of at least one of the oppositelens surfaces of the single lens constituting the third optical elementin the sub scanning direction is reversed from the on-axis toward theoff-axis,

(2-1-3) that the curvatures of the opposite lens surfaces of the singlelens constituting the third optical element in the sub scanningdirection are varied asymmetrically with respect to the optical axisfrom the on-axis toward the off-axis, and

(2-1-4) that the third optical element is made by plastic molding, or

(2-1-5) that the third optical element is made by glass molding.

(2-2) a multibeam scanning optical apparatus in which a plurality ofindependently modulated beams of light emitted from light source meansare imaged into a linear shape long in the main scanning direction onthe deflecting surface of a deflecting element through a first opticalelement and a second optical element and the plurality of beams of lightdeflected by the deflecting element are imaged into a spot-like shape ona surface to be scanned through a third optical element is characterizedin

that the third optical element is comprised of at least two lenses, andthe curvatures of at least two lens surfaces of the two lenses in thesub scanning direction are continuously varied from the on-axis towardthe off-axis to thereby suppress any change of F number in thesub-scanning direction due to the image height of the beam of lightincident on the surface to be scanned.

Particularly, it is characterized in

(2-2-1) that when the maximum value and minimum value of the F number ofthe beam of light incident on the surface to be scanned in thesub-scanning direction are Fmax and Fmin, respectively, the curvaturesof at least two lens surfaces of the two lenses constituting the thirdoptical element in the sub scanning direction are continuously variedfrom the on-axis toward the off-axis so as to satisfy the condition thatFmin/Fmax≧0.9,

(2-2-2) that the sign of the curvature of at least one lens surface ofthe two lenses constituting the third optical element in the subscanning direction is reversed from the on-axis toward the off-axis,

(2-2-3) that the curvatures of at least two surfaces of the two lensesconstituting the third optical element in the sub scanning direction arevaried asymmetrically with respect to the optical axis from the on-axistoward the off-axis, and

(2-2-4) that at least one of the two lenses constituting the thirdoptical element is made by plastic molding, or

(2-2-5) that at least one of the two lenses constituting the thirdoptical element is made by glass molding.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of the essential portions of the opticalsystem of a scanning optical apparatus according to the prior art.

FIGS. 2A and 2B are cross-sectional views of the essential portions ofthe scanning optical apparatus according to the prior art in the mainscanning direction and the sub scanning direction, respectively.

FIG. 3 is a cross-sectional view of the essential portions of a scanningoptical apparatus between a deflecting element and a surface to bescanned in the main scanning direction.

FIGS. 4A and 4B are cross-sectional views of the essential portions ofEmbodiment 1 of the present invention in the main scanning direction andthe sub scanning direction, respectively.

FIG. 5 is an illustration showing the aspherical surface shape of an fθlens in Embodiment 1 of the present invention.

FIG. 6 is an illustration showing the shape of the fθ lens in Embodimenta of the present invention in the main scanning direction.

FIG. 7 is an illustration showing the defocus characteristic of a spotdiameter in the sub scanning direction on a surface to be scanned inEmbodiment 1 of the present invention.

FIGS. 8A and 8B are cross-sectional views of the essential portions ofEmbodiment 2 of the present invention in the main scanning direction andthe sub scanning direction, respectively.

FIG. 9 is an illustration showing the aspherical surface shape of an fθlens in Embodiment 2 of the present invention.

FIG. 10 is an illustration showing the defocus characteristic of thespot diameter in the sub scanning direction on a surface to be scannedin Embodiment 2 of the present invention.

FIG. 11 is an illustration showing the defocus characteristic of a spotdiameter in the sub scanning direction on a surface to be scanned inEmbodiment 2 of the present invention.

FIGS. 12A and 12B are cross-sectional views of the essential portions ofEmbodiment 3 of the present invention in the main scanning direction andthe sub scanning direction, respectively.

FIG. 13 is an illustration showing the aspherical surface shape of an fθlens in Embodiment 3 of the present invention.

FIG. 14 is an illustration showing the shape of the fθ lens in the mainscanning direction in Embodiment 3 of the present invention.

FIG. 15 is an illustration showing the curve of a scanning line inEmbodiment 3 of the present invention.

FIGS. 16A and 16B are cross-sectional views of the essential portions ofEmbodiment 4 of the present invention in the main scanning direction andthe sub scanning direction, respectively.

FIG. 17 is an illustration showing a change in F number in the subscanning direction on a surface to be scanned relative to image heightin Embodiment 4 of the present invention.

FIG. 18 is an illustration showing the curvature of an fθ lens in themeridian-line direction relative to image height in Embodiment 4 of thepresent invention.

FIG. 19 is an illustration showing the curvature of a scanning lineduring multibeam scanning at resolution 600 dpi (scanning line interval42.3 μm) in Embodiment 4 of the present invention.

FIGS. 20A and 20B are cross-sectional views of the essential portions ofEmbodiment 5 of the present invention in the main scanning direction andthe sub scanning direction, respectively.

FIG. 21 is an illustration showing a change of F number in the subscanning direction on a surface to be scanned relative to image heightin Embodiment 5 of the present invention.

FIG. 22 is an illustration showing the curvature of an fθ lens in themeridian-line direction relative to image height in Embodiment 5 of thepresent invention.

FIG. 23 is an illustration showing the curve of a scanning line duringmultibeam scanning at resolution 600 dpi (scanning line interval 42.3μm) in Embodiment 5 of the present invention.

FIGS. 24A and 24B are cross-sectional views of the essential portions ofEmbodiment 6 of the present invention in the main scanning direction andthe sub scanning direction, respectively.

FIG. 25 is an illustration showing a change of F number in the subscanning direction on a surface to be scanned relative to image heightin Embodiment 6 of the present invention.

FIG. 26 is an illustration showing the curvature of an fθ lens in themeridian-line direction relative to image height in Embodiment 6 of thepresent invention.

FIG. 27 is an illustration showing the curve of a scanning line duringmultibeam scanning at resolution 600 dpi (scanning line interval 42.3μm) in Embodiment 6 of the present invention.

FIGS. 28A and 28B are cross-sectional views of the essential portions inthe main scanning direction and the sub scanning direction,respectively, when multibeam scanning was effected by the use of theprior-art single beam scanning optical apparatus shown in FIGS. 2A and2B.

FIG. 29 is an illustration showing a change of F number in the subscanning direction on a surface to be scanned relative to image heightin the single beam scanning optical apparatus shown in FIGS. 28A and28B.

FIG. 30 is an illustration showing the curvature of an fθ lens in themeridian-line direction relative to image height in the single beamscanning optical apparatus shown in FIGS. 28A and 28B.

FIG. 31 is an illustration showing the curve of a scanning line duringmultibeam scanning at resolution 600 dpi (scanning line interval 42.3μm) in the single beam scanning optical apparatus shown in FIGS. 28A and28B.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Before some embodiments of the scanning optical apparatus of the presentinvention are described, means for achieving the objects of the presentinvention will first be described. To achieve the above-describedobjects in the scanning optical apparatus, it is necessary to optimizethe lens shape of the fθ lens and to uniformize the lateralmagnifications in the sub scanning direction on the axis and off theaxis. FIG. 3 is a cross-sectional view of the essential portions in themain scanning direction between the light deflector (deflecting element)of the scanning optical apparatus and the surface to be scanned. Touniformize the lateral magnifications in the sub scanning direction onthe axis and off the axis, it is necessary to determine the principalplane position so that the ratios of the lengths of optical path on theaxis and off the axis may be equal to each other.

Accordingly, the principal plane position of the fθ lens in the subscanning direction is determined so as to satisfy the followingconditions:Ipri:Epri=Imar:EmarIpri·Emar=Epri·Imar  (a)where

-   -   Ipri: the distance from the deflecting surface of the light        deflector to the front side principal plane in the sub scanning        direction in the on-axis beam;    -   Epri: the distance from the rear side principal plane in the sub        scanning direction to the surface to be scanned in the on-axis        beam;    -   Imar: the distance from the deflecting surface of the light        deflector to the front side principal plane in the sub scanning        direction in the most off-axis beam;    -   Emar: the distance from the rear side principal plane in the sub        scanning direction to the surface to be scanned in the most        off-axis beam.

Generally, the off-axis beam is refracted in the direction of theoptical axis in the main scanning plane in order to satisfy the fθcharacteristic and therefore, a focus 71 in the main scanning plane ofthe principal plane in the sub scanning direction for satisfying theabove expression (a) is a plane curved toward a light deflector 5 offthe axis as shown in FIG. 3. Here, when the curve amount on the mostoff-axis is dx,Emar=(Epri+dx)/cos θimgImar=(Ipri−dx)/cos θporand consequently,

$\begin{matrix}{\mspace{79mu}{{{{{{Ipri}\left( {{Epri} + {dx}} \right)}/\cos}\;\theta\;{img}} = {{{{Epri}\left( {{Ipri} - {dx}} \right)}/\cos}\;\theta\;{img}}}{{{dx}\left( {{{{Ipri} \cdot \cos}\;\theta\;{por}} + {{{Epri} \cdot \cos}\;\theta\;{img}}} \right)} = {{Ipri} \cdot {{Epri}\left( {{\cos\;\theta\;{img}} - {\cos\;\theta\;{por}}} \right)}}}\mspace{79mu}{{dx} = \frac{{Ipri} \cdot {{Epri}\left( {{\cos\;\theta\;{img}} - {\cos\;\theta\;{por}}} \right)}}{{{{Ipri} \cdot \cos}\;\theta\;{por}} + {{{Epri} \cdot \cos}\;\theta\;{img}}}}}} & (b)\end{matrix}$where

-   -   θpor: the angle formed in the main scanning plane by the most        off-axis beam deflected by the light deflector with respect to        the optical axis of the fθ lens;    -   θimg: the angle formed in the main scanning plane by the most        off-axis beam incident on the surface to be scanned with respect        to the optical axis of the fθ lens.

Accordingly, to uniformize the lateral magnification in the sub scanningdirection, it is necessary to set the curve amount dx of the locus ofthe principal plane in the sub scanning direction to a value derivedfrom the above expression (b).

That is, when in an actual scanning optical apparatus, the curve amountsof the loci, in the main scanning plane, of the front side principalplane and the rear side principal plane of an fθ lens in the subscanning direction (the difference in the direction of the optical axisbetween the most off-axis principal plane position and the on-axisprincipal plane position) are xm and xu, respectively, it is desirableto determine the principal plane position so as to satisfy the conditionthatxm≦dx≦xu.  (1)

If the above conditional expression (1) is departed from, irregularitywill occur to the lateral magnification in the sub scanning directionand the change in spot diameter due to image height will become great,and this will pose a problem in practice.

Next, as regards a method of changing the principal plane position inthe sub scanning direction, the deflecting surface of the lightdeflector and the surface to be scanned are brought into opticallyconjugate relationship with each other in the sub scanning direction ofthe fθ lens as previously described to thereby effect the correction ofplane inclination and therefore, the refractive power itself of the fθlens cannot be varied.

Accordingly, the first lens surface (R1 surface) and the second lenssurface (R2 surface) of the fθ lens in the sub scanning direction arebent to thereby effect the movement of the principal plane position. Bythe bending, the principal plane of the lens can be moved without therefractive power of the lens itself being changed and therefore, themeridian line r is continuously changed from the on-axis toward theoff-axis and an optimum lens shape can be provided depending onlocation, whereby the lateral magnification in the sub scanningdirection can be uniformized.

By optimizing the lens shape of the fθ lens in this manner, the F number(F No.) in the sub scanning direction of the beam of light incident onthe surface to be scanned can be uniformized, and the variation in thespot diameter in the sub scanning direction due to image height whichhas heretofore been a problem peculiar to a single-lens fθ lens can beminimized.

Also for a beam of light emerging from a light source (light sourceunit) off the optical axis, the surface to be scanned can be highlyaccurately scanned without causing the curve of the scanning line;whereby there can be provided a scanning optical apparatus suitable alsofor multibeam scanning.

Some embodiments of the present invention will now be described.

FIGS. 4A and 4B are cross-sectional views of Embodiment 1 of the presentinvention in the main scanning direction and the sub scanning direction,respectively.

In these figures, reference numeral 1 designates light source means (alight source unit) comprising, for example, a semiconductor laser.

Reference numeral 2 denotes a collimator lens as a first optical elementwhich converts a divergent beam of light emitted from the light sourcemeans 1 into a convergent beam of light. Reference numeral 3 designatesan aperture stop which regularizes the diameter of the beam of lightpassing therethrough.

Reference numeral 4 denotes a cylindrical lens as a second opticalelement which has predetermined refractive power only in the subscanning direction and causes the beam of light passed through theaperture stop 3 to be imaged as a substantially linear image on thedeflecting surface 5 a of a light deflector (deflecting element) 5 whichwill be described later in the sub scanning section.

Reference numeral 5 designates a light deflector as a deflecting elementwhich comprises, for example, a polygon mirror (rotatable polygonmirror) and is rotated at a predetermined speed in the direction ofarrow A by drive means (not shown) such as a motor.

Reference numeral 6 denotes an fθ lens (imaging optical system) as athird optical element comprising a lens having the fθ characteristic anddisposed more toward the light deflector 5 side than the intermediateportion between the light deflector 5 and a photosensitive drum surface8 as a surface to be scanned. In the present embodiment, the oppositelens surface of the fθ lens 6 both comprise a toric surface which isaspherical in the main scanning plane, and continuously varies thecurvature in the sub scanning plane (a plane containing the optical axisof the third optical element and orthogonal to the main scanning plane)from the on-axis toward the off-axis in the effective portion of thelens. Thereby, in Embodiment 1, the change in F number (F No.) in thesub scanning direction due to the image height of the beam of lightincident on the surface 8 to be scanned, i.e., the change in spotdiameter, is minimized. The fθ lens 6 causes the beam of light based onimage information deflected and reflected by the light deflector 5 to beimaged on the photosensitive drum surface 8 and corrects the planeinclination of the deflecting surface of the light deflector 5.

In Embodiment 1, the fθ lens 6 may be made by plastic molding or may bemade by glass molding.

In Embodiment 1, the divergent beam of light emitted from thesemiconductor laser 1 is converted into a convergent beam of light bythe collimator lens 2, and this beam of light (the quantity of light) islimited by the aperture stop 3 and enters the cylindrical lens 4. Thebeam of light having entered the cylindrical lens 4, in the mainscanning section, emerges therefrom intactly in that state. Also, in thesub scanning section, it converges and is imaged as a substantiallylinear image (a linear image long in the main scanning direction) on thedeflecting surface 5 a of the light deflector 5. The beam of lightdeflected and reflected by the deflecting surface 5 a of the lightdeflector 5 is directed onto the photosensitive drum surface 8 throughthe fθ lens 6 having different refractive powers in the main scanningdirection and the sub scanning direction, and scans the photosensitivedrum surface 8 in the direction of arrow B by the light deflector 5being rotated in the direction of arrow A. Thereby, image recording iseffected on the photosensitive drum 8 which is a recording medium.

In Embodiment 1, the lens shape of the fθ lens in the main scanningdirection is an aspherical surface shape which can be represented by afunction up to the tenth-order, and the lens shape in the sub scanningdirection is comprised of a spherical surface continuously varying inthe direction of image height. The lens shape, when for example, thepoint of intersection between the fθ lens and the optical axis is theorigin and the direction of the optical axis is the X-axis and the axisorthogonal to the optical axis in the main scanning plane is the Y-axisand the axis orthogonal to the optical axis in the sub scanning plane isthe Z-axis, is such that the generating-line direction corresponding tothe main scanning direction can be represented by the followingexpression:

$\begin{matrix}{{X = {\frac{Y^{2}/R}{1 + \left( {1 - {\left( {1 + K} \right)\left( {Y/R} \right)^{2}}} \right)^{1/2}} + {B_{4}Y^{4}} + {B_{6}Y^{6}} + {B_{8}Y^{8}} + {B_{10}Y^{10}}}},} & (c)\end{matrix}$

(where R is the radius of curvature, K, B₄, B₆, B₆ and B₁₀ areaspherical surface coefficients) and the meridian-line directioncorresponding to the sub scanning direction (the direction orthogonal tothe main scanning direction containing the optical axis) can berepresented by the following expression:

$\begin{matrix}{{S = \frac{z^{2}/r^{\prime}}{1 + \left( {1 - \left( {z/r^{\prime}} \right)^{2}} \right)^{1/2}}},} & (d)\end{matrix}$

(where r′=r(1+D₂Y²+D₄Y⁴+D₆Y⁶+D₈Y⁸+D₁₀Y¹⁰).

Table 1 below shows the optical arrangement in Embodiment 1 and theaspherical surface coefficients of the fθ lens 6.

TABLE 1 (Embodiment 1) shape of fθ lens 1st surface 2nd surfacewavelength used λ(nm) 780 R 6.7814E+01 1.6154E+02 refractive index of fθlens n 1.519 K −1.6787E+01 −1.0814E+02 angle of incidence on polygon θi−90 B4 −9.8604E−07 −2.2909E−06 maximum angle of emergence from polygonθmax 45 B6 1.5479E−11 7.1426E−10 polygon - fθ lens e 36 B8 8.7055E−14−3.2030E−13 center thickness of fθ lens d 11 B10 −4.7942E−18 7.9836E−17fθ lens - surface to be scanned Sk 110.5 r −2.7332E+01 −1.1859E+01maximum effective diameter of fθ lens Ymax 42 D2S 1.2604E−03 4.9796E−04focal length of fθ lens ft 213.7 D4S 1.2255E−06 −2.0734E−07 degree ofconvergence of collimator fc 317.3 D6S 8.4502E−10 2.3479E−10 polygon -natural converging point D8S −6.3449E−13 −1.0939E−13 D10S 1.3148E−151.5644E−17 D2E 9.3936E−04 4.4938E−04 D4E 2.027E−06 −4.6627E−08 D6E7.0546E−10 1.1322E−10 D8E −1.2936E−12 −5.8704E−14 D10E 2.3372E−154.3944E−18

FIG. 5 is an illustration showing a change of curvature in the subscanning direction relative to the position of the fθ lens 6 in thelengthwise direction. As shown in FIG. 5, the curvature of the meniscusshape is sharp on the axis and becomes plano-convex from the on-axistoward the off-axis. FIG. 6 is an illustration showing the asphericalsurface shape of the fθ lens 6. In FIG. 6, thick solid lines indicatethe lens surface shapes in the main scanning direction, and thin solidlines are the loci of the principal plane in the sub scanning direction,and indicate the front side principal plane and the rear side principalplane.

In Embodiment 1, the curve amount dx of the locus of the principal planefor suppressing the change of lateral magnification in the sub scanningdirection due to image height isdx=6.50fromIpri=48.73 Epri=108.77θpor=44.4° θimg=29.10°.Also, the curve amount xm of the locus of the front side principal planeof the fθ lens 6 in the sub scanning direction and the curve amount xuof the locus of the rear side principal plane thereof arexm=3.24 xu=7.48and these values satisfy the aforementioned conditional expression (1)(xm≦dx≦xu).

Thereby, in Embodiment 1, the lateral magnification in the sub scanningdirection between the light deflector 5 and the surface 8 to be scannedcan be uniformized on the axis and off the axis to a level free of anypractical problem, and as shown in FIG. 7, the change of the spotdiameter in the sub scanning direction due to image height can beminimized. Thereby, there is achieved a scanning optical apparatus whichis inexpensive and suitable for highly accurate printing.

FIGS. 8A and 8B are cross-sectional views of Embodiment 2 of the presentinvention in the main scanning direction and the sub scanning direction,respectively. In FIGS. 8A and 8B, the same elements as the elementsshown in FIGS. 4A and 4B are given the same reference numerals.

The differences of Embodiment 2 from the aforedescribed Embodiment 1 arethat the divergent beam of light emitted from the semiconductor laser(the light source unit) is converted not into a convergent beam of lightbut into a parallel beam of light by the collimator lens and thatcorresponding thereto, the lens shape of the fθ lens is made different.In the other points, the construction and optical action of Embodiment 2are substantially similar to those of Embodiment 1, whereby a similareffect is obtained.

Table 2 below shows the optical arrangement in Embodiment 2 and theaspherical surface coefficients of an fθ lens 26.

TABLE 2 (Embodiment 2) shape of fθ lens 1st surface 2nd surfacewavelength used λ(nm) 780 R 2.2000E+02 −1.1768E+02 refractive index offθ lens n 1.519 K 0.0000E+00 0.0000E+00 angle of incidence on polygon θi−60 B4 −1.1899E−06 −5.2353E−07 maximum angle of emergence from polygonθmax 42 B6 3.1847E−10 −8.6171E−11 polygon - fθ lens e 40 B8 −2.9372E−141.8432E−14 center thickness of fθ lens d 15 B10 3.2427E−19 8.4808E−18 fθlens - surface to be scanned Sk 146.45 r −1.1312E+02 −1.7832E+01 maximumeffective diameter of fθ lens Ymax 43 d2S −4.8301E−04 4.5963E−05 focallength of fθ lens ft 150 d4S 1.8211E−07 −7.1210E−08 d6S −1.0230E−101.7390E−11 d8S 7.2371E−14 −4.3029E−15 d10S −2.1962E−17 −1.4545E−19 d2E−7.0160E−04 1.1994E−05 d4E 3.6411E−07 −5.9970E−08 d6E −1.0351E−11−1.7699E−12 d8E −7.6585E−14 2.1846E−14 d10E 2.0350E−17 −9.2552E−18

FIG. 9 is an illustration showing a change of curvature in the subscanning direction relative, to the position of the fθ lens 26 in thelengthwise direction. As shown in FIG. 9, the curvature of the meniscusshape becomes sharper from the on-axis toward the off-axis. FIG. 10 isan illustration showing the aspherical surface shape of the fθ lens 26.In FIG. 10, thick solid lines indicate the lens surface shape in themain scanning direction, and thin solid lines are the loci of theprincipal plane in the sub scanning direction, and indicate the frontside principal plane and the rear side principal plane.

In Embodiment 2, the curve amount dx of the locus of the principal planefor suppressing the change of lateral magnification in the sub scanningdirection due to image height isdx=7.60fromIpri=53.94 Epri=147.51θpor=42.0° θimg=24.57°.Also, the curve amount xm of the locus of the front side principal planeof the fθ lens 26 in the sub scanning direction and the curve amount xuof the locus of the rear side principal plane thereof arexm=7.34 xu=12.31and these values satisfy the aforementioned conditional expression (1)(xm≦dx≦xu).

Thereby, in Embodiment 2, as in the aforedescribed embodiment 1, thelateral magnification in the sub scanning direction between the lightdeflector 25 and the surface 8 to be scanned can be uniformized on theaxis and off the axis to a level free of any practical problem, and asshown in FIG. 11, the change of the spot diameter in the sub scanningdirection due to image height can be minimized. Thereby, there isachieved a scanning optical apparatus which is inexpensive and suitablefor highly accurate printing.

In Embodiment 2, the divergent beam of light emitted from thesemiconductor laser 1 is converted into a parallel beam of light by thecollimator lens 2 as previously described and therefore, the jitter bythe light deflector is null, and the lens shape, in the main scanningdirection, of the lens surface R2 preponderantly creating the power inthe sub scanning direction is similar to the shape of the locus of theprincipal plane for uniformizing the lateral magnification andtherefore, the lateral magnification can be uniformized even if thechange of curvature in the meridian-line direction due to image heightis small, whereby there can be achieved a scanning optical apparatussuitable for further highly accurate printing.

FIGS. 12A and 12B are cross-sectional views of Embodiment 3 of thepresent invention in the main scanning direction and the sub scanningdirection, respectively. In these figures, the same element as theelements shown in FIG. 4 are given the same reference numerals.

The differences of Embodiment 3 from the aforedescribed Embodiment 1 arethat the apparatus is comprised of a multibeam scanning optical systemfor scanning a plurality of beams of light emitted from light sourcemeans 11 having a plurality of (in Embodiment 3, too) light source unitscapable of being independently modulated, at a time, so as to have apredetermined interval therebetween on the surface to be scanned, andthat correspondingly thereto, the lens shape of the fθ lens in themeridian-line direction (the sub scanning direction) is made different.In the other points, the construction and optical action of Embodiment 3are substantially similar to those of the aforedescribed Embodiment 1,whereby a similar effect is obtained. The above-described plurality oflight source units are disposed at a predetermined interval in the subscanning direction.

Table 3 below shows the optical arrangement in Embodiment 3 and theaspherical surface coefficients of the fθ lens 36.

TABLE 3 (Embodiment 3) shape of fθ lens 1st surface 2nd surfacewavelength used λ(nm) 780 R 6.7814E+01 1.6154E+02 refractive index of fθlens n 1.519 K −1.6787E+01 −1.0814E+02 angle of incidence on polygon θi−90 B4 −9.8604E−07 −2.2909E−06 maximum angle of emergence from polygonθmax 45 B6 1.5479E−11 7.1426E−10 polygon - fθ lens e 36 B8 8.7055E−14−3.2030E−13 center thickness of fθ lens d 11 B10 −4.7942E−18 7.9836E−17fθ lens - surface to be scanned Sk 110.5 r −2.8363E+01 −1.1966E+01maximum effective diameter of fθ lens Ymax 42 d2S 5.4992E−05 4.4462E−05focal length of fθ lens ft 213.7 d4S −2.2581E−08 −2.7866E−08 degree ofconvergence of collimator fc 317.3 d6S 9.5892E−12 2.5295E−11 polygon -natural converging point d8S −1.9648E−15 −1.0163E−14 d10S 2.7992E−191.9816E−18 d2E 4.3102E−05 3.9194E−05 d4E 1.7579E−08 −1.2704E−08 d6E−3.6419E−11 1.1605E−11 d8E 2.1285E−14 −3.3827E−15 d10E −4.6427E−188.2100E−20

In Embodiment 3, the lens shape of at least one of the lens surfaces ofthe fθ lens 36 in the meridian-line direction is set so that the sign ofcurvature may be reversed from on the on-axis toward the off-axis.Therefore, the meridian-line direction of the fθ lens 36 correspondingto the sub scanning direction is represented by the followingexpression:

$\begin{matrix}{{S = \frac{z^{2}/r^{\prime}}{1 + \left( {1 - \left( {z/r^{\prime}} \right)^{2}} \right)^{1/2}}},} & (e)\end{matrix}$where r′=r+d₂Y²+d₄Y⁴+d₆Y⁶+d₈Y⁸d₁₀Y¹⁰. Also, the generating-linedirection corresponding to the main scanning direction is represented byexpression (c) as in the aforedescribed Embodiment 1.

FIG. 13 is an illustration showing a change of curvature in the subscanning direction relative to the position of the fθ lens 36 inEmbodiment 3 in the lengthwise direction. As shown in FIG. 13, on thelens surface R1, the sign of curvature in the sub scanning direction isreversed from on the on-axis toward the off-axis, and the meniscus shapeon the axis changes into a biconvex shape off the axis. FIG. 14 is anillustration showing the aspherical surface shape of the fθ lens 36. InFIG. 14, thick solid lines indicate the lens surface shape in the mainscanning direction, and thin solid lines are the loci of the principalplane in the sub scanning direction, and indicate the front sideprincipal plane and the rear side principal plane.

In Embodiment 3, the curve amount dx of the locus of the principal planefor suppressing the change of lateral magnification in the sub scanningdirection due to image height isdx=6.50fromPpri=48.73 Epri=108.77θpor=44.4° θimg=29.10°.Also, the curve amount xm of the locus of the front side principal planeof the fθ lens 36 in the sub scanning direction and the curve amount xuof the locus of the rear side principal plane thereof arexm=4.93 xu=9.10and these values satisfy the aforementioned conditional expression (1)(xm≦dx≦xu).

Thus, in Embodiment 3, as in the aforedescribed Embodiments 1 and 2, thelateral magnification in the sub scanning direction between the lightdeflector 5 and the surface 8 to be scanned can be uniformized to alevel free of any practical problem on the axis and off the axis, andthe change of the spot diameter in the sub scanning direction due toimage height can be minimized. Thereby, there is achieved a scanningoptical apparatus which is inexpensive and suitable for highly accurateprinting.

Also, Embodiment 3 is a multibeam scanning optical apparatus using aplurality of beams of light to scan the surface to be scanned at a timeand therefore, the curve of the scanning line provides pitchirregularity on the image and this is not good.

So, in Embodiment 3, the radius of curvature in the sub scanningdirection is continuously varied in the effective portion of the lens byimage height, whereby the curve of the scanning line on the surface tobe scanned can be eliminated as shown in FIG. 15, and thus, there isachieved a scanning optical apparatus (multibeam scanning opticalapparatus) of high image quality free of pitch irregularity.

FIGS. 16A and 16B are cross-sectional views of the essential portions ofEmbodiment 4 of the present invention in the main scanning direction andthe sub scanning direction, respectively. In these figures, the sameelement as the elements shown in FIGS. 12A and 12B are given the samereference numerals.

In FIGS. 16A and 16B, reference numeral 46 designates an fθ lens (animaging optical system) comprising a lens having the fθ characteristicas a third optical element, and this fθ lens 46 is disposed more towardthe light deflector 5 than the intermediate portion between the lightdeflector 5 and the photosensitive drum surface 8 as the surface to bescanned.

In Embodiment 4, the opposite lens surfaces of the fθ lens 46 both havetheir curvatures in the sub scanning direction continuously varied fromthe on-axis fθ lens 46 both have their curvatures in the sub scanningdirection continuously varied from the on-axis toward the off-axis.Thereby, in Embodiment 4, the change of F number in the sub scanningdirection due to the image height of the beam of light incident on thesurface to be scanned, i.e., the change of the spat diameter, isminimized. Also, the sign of the curvature of at least one (the firstsurface) R1 of the opposite lens surfaces of the fθ lens 46 in the subscanning direction is reversed from the on-axis toward the off-axis.Further, the curvatures of the opposite lens surfaces of the fθ lens inthe sub scanning direction are varied from the on-axis toward theoff-axis so as to become asymmetrical with respect to the optical axis.The fθ lens 46 causes a plurality of beams of light based on imageinformation deflected and reflected by the light deflector 5 to beimaged on the photosensitive drum surface 8 and corrects the planeinclination of the deflecting surface of the light deflector 5.

In Embodiment 4, the fθ lens 46 may be made by plastic molding or may bemade by glass molding.

In Embodiment 4, two independently modulated divergent beams of lightemitted from a semiconductor laser 11 are converted into convergentbeams of light by the collimator lens 2, and these beams of light (thequantity of light) are limited by the aperture stop 3 and enter thecylindrical lens 4. The beams of light having entered the cylindricallens 4, in the main scanning section, emerge therefrom intactly in thatstate. Also, in the sub scanning section, they converge and are imagedas substantially linear images (linear images long in the main scanningdirection) on the deflecting surface 5 a of the light deflector 5. Thetwo beams of light deflected and reflected by the deflecting surface 5 aof the light deflector 5 from two spots on the photosensitive drumsurface 8 through the fθ lens 46 having different refractive powers inthe main scanning direction and the sub scanning direction, and scan thephotosensitive drum surface 8 in the direction of arrow B by the lightdeflector 5 being rotated in the direction of arrow A. Thereby, imagerecording is effected.

In Embodiment 4, the lens shape of the fθ lens 46, in the main scanningdirection, is made into an aspherical surface shape capable of beingrepresented by a function up to the 10th order in the main scanningdirection and in the sub scanning direction, is comprised of a sphericalsurface continuously varying in the image height direction. That lensshape is such that the generating-line direction corresponding to themain scanning direction is indicated by the aforementioned expression(c) and the meridian-line direction corresponding to the sub scanningdirection (the direction orthogonal to the main scanning directioncontaining the optical axis of the fθ lens) can be represented by

$\begin{matrix}{{S = \frac{z^{2}/r^{\prime}}{1 + \left( {1 - \left( {z/r^{\prime}} \right)^{2}} \right)^{1/2}}},} & (f)\end{matrix}$

(where 1/r′=1/r+D₂Y²+D₄Y⁴+D₆Y⁶+D₈Y⁸+D₁₀Y¹⁰)

Generally, in a multibeam scanning optical apparatus, to make pitchirregularity visually inconspicuous, it is desirable that the pitchirregularity due to the curve of the scanning line be 1/10 of the beampitch in the sub scanning direction or less. For example, in the case ofa scanning optical apparatus in which the resolution in the sub scanningdirection is 600 dpi, the beam pitch in the sub scanning direction is 42μm and therefore, allowable pitch irregularity is about 4 μm or less.

So, in Embodiment 4, when the maximum value and the minimum value of theF number of the beam of light incident on the surface to be scanned inthe sub scanning direction are Fmax and Fmin, respectively, thecurvatures of the opposite lens surfaces of the fθ lens 46 in the subscanning direction are continuously varied from the on-axis toward theoff-axis so as to satisfy the condition thatFmin/Fmax≧0.9,  (2)whereby the curve of the scanning line can be eliminated to therebyachieve a multibeam scanning optical apparatus which suffers little frompitch irregularity and is high in image quality and compact.

If the above-mentioned condition is departed from, pitch irregularitywill become visually conspicuous due to the curve of the scanning lineand this will pose a problem in practice.

Table 4 below shows the optical arrangement in Embodiment 4 and theaspherical surface coefficients of the fθ lens 46.

TABLE 4 (Embodiment 4) shape of fθ lens Design Data 1st surface 2ndsurface wavelength used λ(nm) 780 R 6.7814E+01 1.6154E+02 refractiveindex of fθ lens n 1.519 K −1.6787E+01 −1.0814E−02 angle of incidence onpolygon θi −90 B4 −9.8604E−07 −2.2909E−06 maximum angle of emergencefrom polygon θmax 45 B6 1.5479E−11 7.1426E−10 polygon - fθ lens e 36 B88.7055E−14 −3.2030E−13 center thickness of fθ lens d 11 B10 −4.7942E−187.9836E−17 fθ lens - surface to be scanned Sk 110.5 r −2.8363E+01−1.1966E+01 maximum effective diameter of fθ lens Ymax 42 D2S 5.4992E−054.4462E−05 focal length of fθ lens ft 213.7 D4S −2.2581E−08 −2.7866E−08degree of convergence of collimator fc 317.3 D6S 9.5892E−12 2.5295E−11polygon - natural converging point D8S −1.9648E−15 −1.0163E−14 polygoncircumscribed circle φ20 4 surfaces D10S 2.7992E−19 1.9816E−18 D2E4.3102E−05 3.9194E−05 D4E 1.7579E−08 −1.2704E−08 D6S −3.6419E−111.1605E−11 D8E 2.1285E−14 −3.3827E−15 D10E −4.6427E−18 8.2100E−20

FIG. 17 is an illustration showing a change of F number in the subscanning direction on the surface to be scanned in Embodiment 4. InEmbodiment 4, the curvatures of the fθ lens 46 in the sub scanningdirection are continuously varied on the opposite lens surfaces from theon-axis toward the off-axis as shown in FIG. 18 to thereby suppress therate of change of F number due to image height so as to beFmin/Fmax=64.52/66.31=0.973,i.e., 0.9 or greater.

FIG. 19 is an illustration showing the curve of the scanning line whenthe multibeam scanning optical apparatus of Embodiment 4 is used atresolution 600 dpi (scanning line interval 42.3 μm). By suppressing thechange of F number due to image height as described above, the curve ofthe scanning line can be brought to a level of the order of 0.2 μm(pitch irregularity being of the order of 0.4 μm) which is quite free ofpractical problem.

Thus, in Embodiment 4, as described above, conditional expression (2) issatisfied and yet the curvatures of the fθ lens 46 in the sub scanningdirection (the meridian-line direction) are continuously varied from theon-axis toward the off-axis to thereby suppress the change of F numberin the sub scanning direction due to image height, i.e., the change ofthe spot diameter, to below a predetermined amount (within the allowablevalue of the apparatus) and eliminate the pitch irregularity due to thecurve of the scanning line which poses a problem in the multibeamscanning optical apparatus. Also, in Embodiment 4, the third opticalelement (fθ lens) 46 is comprised of a single lens and therefore, therecan be achieved a compact and low-cost multibeam scanning opticalapparatus.

FIGS. 20A and 20B are cross-sectional views of the essential portions ofEmbodiment 5 of the present invention in the main scanning direction andthe sub scanning direction, respectively. In these figures, the sameelements as the elements shown in FIGS. 12A and 12B are given the samereference numerals.

The differences of Embodiment 5 from the aforedescribed Embodiment 4 arethat in order to make curvature of image field in the main scanningdirection small so as to be capable of coping with further highlyaccurate printing, the curvatures of the opposite lens surfaces of an fθlens 56 in the generating-line direction are set so as to beasymmetrical with the optical axis, and that the number of the polygonsurfaces of the polygon mirror 15 is changed from four to six to therebycope with high-speed printing. In the other points, the construction andoptical action of Embodiment 5 are substantially similar to those ofEmbodiment 4, whereby a similar effect is obtained.

Table 5 below shows the optical arrangement in Embodiment 5 and theaspherical surface coefficients of the fθ lens 56.

TABLE 5 (Embodiment 5) shape of fθ lens Design Data 1st surface 2ndsurface wavelength used λ(nm) 780 R 7.6014E+01 1.8577E+02 refractiveindex of fθ lens n 1.524 K −1.4188E+01 −9.3624E+01 angle of incidence onpolygon θi −60 B4S −8.8268E−07 −1.6683E−06 maximum angle of emergencefrom polygon θmax 41.0 B6S 8.8566E−11 3.5647E−10 polygon - fθ lens e41.1 B8S 4.0586E−14 −1.2120E−13 center thickness of fθ lens d 10.4 B10S−5.2861E−19 3.5062E−17 fθ lens - surface to be scanned Sk 122.5 B4E−8.8268E−07 −1.6683E−06 maximum effective diameter of fθ lens Ymax 42B6E 5.2038E−11 3.5647E−10 focal length of fθ lens ft 237.7 B8E6.4399E−14 −1.2120E−13 degree of convergence of collimator fc 339.69B10E −5.1518E−18 3.5062E−17 polygon - natural converging point r−3.0459E+01 −1.3017E+01 polygon circumscribed circle φ40 6 surfaces D2S−3.2380E−05 −1.4111E−06 D4S 7.6080E−08 1.0715E−09 D6S −3.4870E−111.7648E−11 D8S 5.0570E−15 −8.2750E−15 D10S 0.0000E+00 1.0082E−18 D2E−3.5200E−05 −1.4111E−06 D4E 8.0516E−08 1.0715E−09 D6E −3.8015E−111.7648E−11 D8E 6.0665E−15 −8.2750E−15 D10E −1.1908E−19 1.0082E−18

FIG. 21 is an illustration showing a change of F number in the subscanning direction on the surface to be scanned in Embodiment 5. InEmbodiment 5, the curvatures of the fθ lens 56 in the sub scanningdirection are continuously varied on the opposite lens surfaces from theon-axis toward the off-axis as shown in FIG. 22, to thereby suppress therate of change of F number due to image height so as to beFmin/Fmax=49.75/53.08=0.937,i.e., 0.9 or greater.

FIG. 23 is an illustration showing the curve of the scanning line whenthe multibeam scanning optical apparatus of Embodiment 5 is used atresolution 600 dpi (the scanning line interval 42.3 μm). By suppressingthe change of F number due to image height as described above, the curveof the scanning line can be brought to a level of the order of 1.2 μm(the pitch irregularity being of the order of 2.4 μm) quite free of apractical problem.

Thus, again in Embodiment 5, as in Embodiment 4, conditional expression(2) is satisfied and yet the curvatures of the opposite lens surfaces ofthe fθ lens 56 in the sub scanning direction (the meridian-linedirection) are continuously varied from the on-axis toward the off-axisto thereby suppress the change of F number in the sub scanning directiondue to image height, i.e., the change of the spot diameter, to below apredetermined amount, and eliminate the pitch irregularity due to thecurve of the scanning line which poses a problem in the multibeamscanning optical apparatus. Also, in Embodiment 5, the curvatures of theopposite lens surfaces of the fθ lens (the third optical element) 56 inthe generating-line direction are set so as to be asymmetrical withrespect to the optical axis to thereby suppress the curvature of imagefield in the main scanning direction and achieve a multibeam scanningoptical apparatus suitable for further highly accurate printing.

FIGS. 24A and 24B are cross-sectional views of the essential portions ofEmbodiment 6 of the present invention in the main scanning direction andthe sub scanning direction, respectively. In these figures, the sameelement as the elements shown in FIGS. 12A and 12B are given the samereference numerals.

The differences of Embodiment 6 from the aforedescribed Embodiment 4 arethat an fθ lens (the third optical element) 76 is comprised of twolenses and the pitch irregularity due to the curve of the scanning lineis reduced at higher accuracy, that the beam of light from asemiconductor laser 11 having a plurality of light emitting portionscapable of being independently modulated is converted into asubstantially parallel beam of light by the collimator lens 2, and thatthe number of the polygon surfaces of the polygon mirror 15 is changedfrom four to six to thereby cope with high-speed printing. In the otherpoints, the construction and optical action of Embodiment 6 aresubstantially similar to those of the aforedescribed Embodiment 4,whereby a similar effect is obtained.

That is, in FIGS. 24A and 24B, reference numeral 76 designates an fθlens as a third optical element, which comprises two lenses, i.e., aspherical lens (glass spherical lens) 76 a as a first fθ lens formed ofa glass material, and a toric lens (aspherical plastic toric lens) 76 bas a second fθ lens of an aspherical surface shape formed of a plasticmaterial. The glass spherical lens 76 a is disposed more toward thelight deflector 15 than the intermediate portion between the lightdeflector 15 and the photosensitive drum surface 8 and has the functionof correcting chiefly the fθ characteristic. The aspherical plastictoric lens 76 b effects chiefly the correction of curvature of imagefield and the correction of lateral magnification in the sub scanningdirection.

In Embodiment 6, the curvatures, in the meridian-line direction (the subscanning direction), of the opposite lens surfaces of the asphericalplastic toric lens 76 b bearing almost all of the refractive power inthe sub scanning direction are continuously varied from the on-axistoward the off-axis to thereby suppress the change of F number in thesub scanning direction on the surface to be scanned, i.e., the change ofthe spot diameter.

Table 6 below shows the optical arrangement in Embodiment 6 and theaspherical surface coefficients of the fθ lens (spherical lens 76 a andtoric lens 76 b) 76.

TABLE 6 (Embodiment 6) shape of 1st fθ lens Design Data 1st surface 2ndsurface wavelength used λ(nm) 780 R ∞ −1.2042E+02 refractive index of1st fθ lens n1 1.786 r ∞ −1.2042E+02 refractive index of 2nd fθ lens n21.572 shape of 2nd fθ lens angle of incidence on polygon θi 65 1stsurface 2nd surface maximum angle of emergence from polygon θmax 45 R−8.7734E+02 −3.4387E+02 polygon - 1st fθ lens e1 25.28 K 0.0000E+00 0.0000E+00 center thickness of 1st fθ lens d1 14.00 B4 −1.5203E−08  6.2830E−0.8 focal length of 1st to 2nd fθ lens e2 17.60 B6 −1.2062E−11−1.5527E−11 center thickness of 2nd fθ lens d2 5.10 r −1.2218E+01−9.9688E+00 fθ lens - surface to be scanned Sk 116.13 D2S −4.2145E−07 4.2877E−07 maximum effective diameter of fθ lens Ymax 50 D4S 1.3072E−10−7.9350E−10 focal length of fθ lens ft 136 D6S 6.7762E−13  7.0965E−13polygon circumscribed circle φ40 6 surfaces D2E 2.2156E−07  1.2975E−07D4E 1.2193E−11 −2.2874E−10 D6E 4.9138E−13  4.3863E−13

FIG. 25 is an illustration showing a change of F number in the subscanning direction on the surface to be scanned in Embodiment 6. InEmbodiment 6, the curvatures of the toric lens 76 b in the sub scanningdirection are continuously varied on the opposite lens surfaces thereoffrom the on-axis toward the off-axis as shown in FIG. 26 to therebysuppress the rate of change of F number due to image height so as to beFmin/Fmax=72.67/73.75=0.985,i.e., 0.9 or greater.

FIG. 27 is an illustration showing the curve of the scanning line whenthe multibeam scanning optical apparatus of Embodiment 6 is used atresolution 600 dpi (scanning line interval 42.3 μm). By suppressing thechange of F number due to image height, the curve of the scanning linecan be brought to a level of the order of 0.1 μm (pitch irregularitybeing of the order of 0.2 μm) free of a practical problem.

Thus, again in Embodiment 6, as in the aforedescribed Embodiment 4,conditional expression (2) is satisfied and yet the curvatures of theopposite lens surfaces of the toric lens 76 b constituting the fθ lens76 in the sub scanning direction (the meridian-line direction) arecontinuously varied from the on-axis toward the off-axis to therebysuppress the change of F number in the sub scanning direction due toheight, i.e., the change of the spot diameter, to below a predeterminedamount and eliminate the pitch irregularity due to the curve of thescanning line which poses a problem in the multibeam scanning opticalapparatus. Also, in Embodiment 6, by the fθ lens (the third opticalelement) 76 being comprised of two lenses, the curve of the scanningline can be corrected more highly accurately, and there is achieved amultibeam scanning optical apparatus suitable for further highlyaccurate printing.

The sign of the curvature of at least one of the two lenses constitutingthe third optical element in the sub scanning direction may be reversedfrom the on-axis toward the off-axis, and the curvatures of at least twolens surfaces of the two lenses in the sub scanning direction may bevaried asymmetrically with respect to the optical axis from the on-axistoward the off-axis. Thereby, there can be achieved a multibeam scanningoptical apparatus more suitable for highly accurate printing.

Lastly, for the comparison with the scanning optical apparatus of thepresent invention, description will be made of the manner in whichmultibeam scanning was effected by a single beam scanning opticalapparatus.

FIGS. 28A and 28B are cross-sectional views of the essential portions inthe main scanning direction and the sub scanning direction,respectively, when multibeam scanning was effected by the use of thesingle beam scanning optical apparatus and show the changes of theangular magnification in the sub scanning direction and the spotdiameter (F number) in the sub scanning direction on the surface to bescanned, due to image height. Table 7 below shows the opticalarrangement shown in FIGS. 28A and 28B and the aspherical surfacecoefficients of an fθ lens 86.

TABLE 7 shape of fθ lens Design Data 1st surface 2nd surface wavelengthused λ(nm) 780 R 6.7814E+01 1.6154E+02 refractive index of fθ lens n1.519 K −1.6787E+01 −1.0814E+02 angle of incidence on polygon θi −90 B4−9.8604E−07 −2.2909E−06 maximum angle of emergence from polygon θmax 45B6 1.5479E−11 7.1426E−10 polygon - fθ lens e 36 B8 8.7055E−14−3.2030E−13 center thickness of fθ lens d 11 B10 −4.7942E−18 7.9836E−17fθ lens - surface to be scanned Sk 110.5 r −2.8531E+01 −1.1991E+01maximum effective diameter of fθ lens Ymax 42 D2S 0.0000E+00 2.1635E−05focal length of fθ lens ft 213.7 D4S 0.0000E+00 −3.6548E−08 degree ofconvergence of collimator fc 317.3 D6S 0.0000E+00 2.7926E−11 polygon -natural converging point D8S 0.0000E+00 −1.1184E−14 polygoncircumscribed circle φ20 4 surfaces D10S 0.0000E+00 1.7618E−18 D2E0.0000E+00 2.2817E−05 D4E 0.0000E+00 −3.8012E−03 D6E 0.0000E+002.9368E−11 D8E 0.0000E+00 −1.2060E−14 D10E 0.0000E+00 1.9700E−18

In FIGS. 28A and 28B, two in dependently modulated divergent beams oflight emitted from light source means 81 are converted into convergentbeams of light by a collimator lens 82, and these beams of light (thequantity of light) are limited by a stop 83 and enter a cylindrical lens84 having predetermined refractive power. The beams of light havingentered the cylindrical lens 84, in the main scanning plane, intactlyemerge in that state. Also, in the sub scanning section, they convergeand are imaged as substantially linear images on the deflecting surface(reflecting surface) 85 a of a light deflector 85 comprising a rotatablepolygon mirror. The two beams of light deflected and reflected by thedeflecting surface 85 a of the light deflector 85 are directed onto aphotosensitive drum surface as a surface 88 to be scanned through animaging optical system (fθ lens) 86 having the fθ characteristic, andthe light deflector 85 is rotated in the direction of arrow A, wherebythe photosensitive drum surface 88 is light-scanned to thereby effectthe recording of image information.

Usually, in a plane inclination correcting optical system, as previouslydescribed, it is necessary to bring the deflecting surface of the lightdeflector and the surface to be scanned into optically conjugaterelationship (imaging relationship) with each other in order tooptically correct the plane inclination of the deflecting surface. Inthe comparative example shown in FIGS. 28A and 28B, with the curvaturein the sub scanning direction (meridian line curvature) of that lenssurface (first surface) R1 of the fθ lens 86 which is adjacent to thelight deflector 85 being constant, the curvature in the sub scanningdirection (meridian line curvature) of that lens surface (secondsurface) R2 of the fθ lens 86 which is adjacent to the surface to bescanned is continuously varied from the on-axis toward the off-axis tothereby bring about conjugate relationship at any image height.

However, the fθ lens 86 in the above-described comparative example isconstant in the meridian line curvature of one surface (surface R1)thereof as shown in FIG. 30 and therefore, as shown in FIG. 29,depending on the bus line shape thereof, F number (F No) becomesirregular due to image height. That is, on the axis (the on-axis beam),the F number in the sub scanning direction on the surface to be scannedis great as shown in (1) in FIG. 28B and therefore, the angularmagnification in the sub scanning direction is small, and off the axis(the off-axis beam), the F number in the sub scanning direction is smallas shown in (2) in FIG. 28B and therefore, the angular magnification isgreat (there is a converse case depending on the main scanning planeshape).

Generally, between the angular magnification γ and the lateralmagnification β, the relation thatβγ=−1is established and therefore, in the above-described comparativeexample; the lateral magnification becomes great on the axis and thelateral magnification becomes small off the axis. Therefore, due toimage height, irregularity is created in the lateral magnification inthe sub scanning direction, and in an optical system like a multibeamscanning optical apparatus which uses a plurality of laser beams off theoptical axis to scan, the scanning line makes a curve on the surface tobe scanned.

FIG. 31 is an illustration showing the curve of the scanning line whenthe multibeam scanning optical apparatus of the comparative example isused at resolution 600 dpi (scanning line interval 42.3 μm). In FIG. 31,the scanning line in the marginal portion is curved by 2.4 μm withrespect to the central portion, and this leads to the problem that pitchirregularity of 4.8 μm will result and deteriorate the quality of image.

The above-noted problem does not arise in the scanning optical apparatusof the present invention, and according to a first invention, there canbe achieved a compact scanning optical apparatus suitable for highlyaccurate printing in which when as previously described, a beam of lightfrom a light source converted by a collimator lens or the like is to beimaged on a surface to be scanned by an fθ lens through a lightdeflector, curvature of image field, distortion, etc. are well correctedby optimizing the lens shape of the fθ lens and the non-uniformity ofthe lateral magnification in the sub scanning direction between thelight deflector and the surface to be scanned can be eliminated tothereby suppress the change of F number in the sub scanning directiondue to image height, i.e., the change of the spot diameter.

Also, according to a second invention, there can be achieved a multibeamscanning optical apparatus in which when as previously described, aplurality of beams of light from a light source converted by acollimator lens or the like are to be imaged on a surface to be scannedby an fθ lens through a light deflector, curvature of image field,distortion, etc. are well corrected by optimizing the lens shape of thefθ lens and the non-uniformity of the lateral magnification in the subscanning direction between the light deflector and the surface to bescanned can be eliminated to thereby suppress the change of F number inthe sub scanning direction due to image height, i.e., the change of thespot diameter, and reduce the pitch irregularity due to the curve of thescanning line.

Further, there can be achieved a multibeam scanning optical apparatus inwhich the curvature of the fθ lens in the sub scanning direction isdetermined so as to satisfy the aforementioned conditional expression(2), whereby pitch irregularity can be reduced to a visuallyproblem-free level.

What is claimed is:
 1. A multibeam scanning optical apparatuscomprising: a light source unit for emitting a plurality of light beams;a light deflector for deflecting and reflecting the light beams; and animaging optical system for imaging the light beams deflected by saidlight deflector on a surface to be scanned, wherein said imaging opticalsystem has a plurality of lens surfaces, wherein the light beams areincident on said imaging optical system at positions which are differentin a sub-scanning direction, and curvatures of the lens surfaces in thesub-scanning direction change continuously, independently of thecurvatures in a main-scanning direction and non-symmetrically withrespect to the optical axis of the imaging optical system along themain-scanning direction so that Fmin/Fmax≧0.9 is satisfied, where Fmaxis a maximum value of a F number of the light beam incident on thesurface to be scanned with respect to the sub-scanning direction, andFmin is a minimum value of a F number of the light beam incident on thesurface to be scanned with respect to the sub-scanning direction, andwherein said imaging optical system comprises a single lens.
 2. Amultibeam scanning optical apparatus according to claim 1, wherein thelight beam is incident on the light deflector in a main scanning planein directions inclined relative to a deflecting surface of said lightdeflector.
 3. A multibeam scanning optical apparatus according to claim1, wherein the optical magnification of said imaging optical system inthe sub-scanning direction is constant over the effective scanningregion.
 4. A multibeam scanning optical apparatus according to claim 1,wherein the plurality of light beams include a first light beam and asecond light beam, and wherein curvatures of the lens surfaces in thesub-scanning direction change continuously along the main-scanningdirection so that a pitch unevenness, in the sub-scanning direction,between a scanning line of the first beam and a scanning line of thesecond beam is not more than 1/10.
 5. A laser beam printer comprising amultibeam scanning optical apparatus, said multibeam scanning opticalapparatus including: a light source unit for emitting a plurality oflight beams; a light deflector for deflecting and reflecting the lightbeams; and an imaging optical system for imaging the light beamsdeflected by said light deflector on a surface to be scanned, whereinsaid imaging optical system has a plurality of lens surfaces, whereinthe light beams are incident on said imaging optical system at positionswhich are different in a sub-scanning direction, and curvatures of thelens surfaces in the sub-scanning direction change continuously,independently of the curvatures in a main-scanning direction andnon-symmetrically with respect to the optical axis of the imagingoptical system along the main-scanning direction so that Fmin/Fmax≧0.9is satisfied, where Fmax is a maximum value of a F number of the lightbeam incident on the surface to be scanned with respect to thesub-scanning direction, and Fmin is a minimum value of a F number of thelight beam incident on the surface to be scanned with respect to thesub-scanning direction, wherein the surface to be scanned is a surfaceof a photosensitive drum, and wherein said imaging optical systemcomprises a single lens.